Sound source separation (SSS) is a fundamental problem in audio signal processing, aiming to recover individual audio sources from a given mixture. A promising approach is multichannel non-negative matrix factorization (MNMF), which employs a Gaussian probabilistic model encoding both magnitude correlations and phase differences between channels through spatial covariance matrices (SCM). In this work, we present a dedicated hardware architecture implemented on field programmable gate arrays (FPGAs) for efficient SSS using MNMF-based techniques. A novel decorrelation constraint is presented to facilitate the factorization of the SCM signal model, tailored to the challenges of multichannel source separation. The performance of this FPGA-based approach is comprehensively evaluated, taking advantage of the flexibility and computational capabilities of FPGAs to create an efficient real-time source separation framework. Our experimental results demonstrate consistent, high-quality results in terms of sound separation.